Parameter description: The thickness of the cylinder is the difference between the inner and outer radius. The outer radius always being greater than the inner radius. All parameters are known except for the position vector,"rho", which varies from the inner radius to the outer radius. In the schematic shown below, the inner pressure is greater than the outer pressure, therefore from the equations, the stresses are largest as rho approaches the inner radius. However, if the outer pressure is greater than the inner pressure, the stresses will be largest as rho approaches the outer radius.
As shown in the color image below, the elements that are located at the same radius but different angle theta (elements A and B) will experience the same tangential and radial stresses, this can be easily inferred from the fact that there is no angular positional variable(i.e. theta) in any of the governing equations. However, the elements at different radial lengths experience different stresses, this can be observed from the fact "rho" is a variable in the governing equations.
Stress description: Tangential stress affects the element in a direction tangent to its circumference, i.e. perpendicular to the radial vector. Radial stress affects the element in a direction that is parallel to the radial vector. For any pressure-thickness condition the difference between the tangential and radial stress is a constant for all range of rho. That constant can be arrived by subtracting the radial stress from the tangential stress. Because the tangential stress is always greater the constant will be a positive value.
